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# Modeling Systems of Equations

Lesson 9 of 24

## Objective: Students will be able to solve a real-life scenario using a system of equations.

#### Warm up and Homework Check

*10 min*

I include **Warm ups **with a **Rubric **as part of my daily routine. My goal is to allow students to work on **Math Practice 3 **each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The lesson Warm Up- Modeling Systems of Equations has students to use the structure of equations to find the error in a solved system of equations (**Math Practice 7**).

I also use this time to correct and record the previous day's Homework.

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This lesson is a scaffolding measure to prepare my students for future lessons. The goal is to use systems to model real life situations (**Math Practice 4**). We will come back to this repeated throughout the year. I begin this lesson with a **guided practice** problem to get my students thinking about modeling situations with systems. Here is the problem:

*Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said,*

*I wonder whether the dollar belongs inside the cash box or not.*

*The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?*

This problem comes from Illustrative Mathematics.

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#### Becoming an Expert

*10 min*

The next goal is for each student much become an expert in a systems problem. I have three levels of problems that each pair of students will pick from with level three having several non-linear systems. They have been placed in duplicates so each person can keep a copy. Either they can choose their own level or I will choose it for them. The partners then solve their system together check it with me. It is important that they really understand their problem since they will be helping other students’ efforts on this problem. I also think it is important that they are able to solve it algebraically rather than just graphically as they may be checking the algebraic work of other students.

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Now that the students are masters of a problem, the remainder of the class will be spent on rotating around the classroom solving each other’s problems. This will be worth a homework grade as it is taking the place of a homework assignment. I have desks in rows with partners next to each other so the student on the left side of each pair will rotate around the room in a pattern that I designate. The students may get mixed up at first so vigilance is necessary particularly at the beginning of the activity.

Students will switch and solve each other’s problems. I encourage students to attempt to give hints or ask leading questions rather than just giving steps as the help the people that they are working with (**Math Practice 3**). It is also important that they are comfortable with their peers using methods other than the one they used. Graphing is an acceptable method at this stage. My job is to rotate around helping students stay on track and troubleshooting as necessary. Often with systems, it is difficult to find an error in the steps. This is where I can be helpful. I will identify the issue, share it with the expert and allow them to share it with their partner.

We will rotate as many times as possible. Managing time is important, please see my video on pacing. There may be points when partners will need to be switched before a particular group is finished.

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today’s Exit Ticket asks student to find the solution to a systems word problem.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Mathematical Modeling: Properties of Functions Day 1 of 2
- LESSON 2: Mathematical Modeling: Properties of Functions Day 2 of 2
- LESSON 3: Mathematical Modeling: Linear Functions
- LESSON 4: Mathematical Modeling: Linear Functions Design Project
- LESSON 5: Finding Equations of Parallel and Perpendicular Lines
- LESSON 6: Inverse Functions
- LESSON 7: System of Equations Day 1 of 2
- LESSON 8: Systems of Equations Day 2 of 2
- LESSON 9: Modeling Systems of Equations
- LESSON 10: Function Review
- LESSON 11: Function Mid Test
- LESSON 12: The Tortoise and The Hare Project Day 1
- LESSON 13: The Tortoise and The Hare Project Day 2
- LESSON 14: The Tortoise and The Hare Project Day 3
- LESSON 15: The Tortoise and the Hare Project Day 4
- LESSON 16: The Tortoise and the Hare Piece-wise Functions
- LESSON 17: Step Functions
- LESSON 18: Absolute Value Equations
- LESSON 19: Absolute Value Inequalities
- LESSON 20: Absolute Value Functions: Transformations Day 1
- LESSON 21: Absolute Value Functions: Transformations Day 2
- LESSON 22: Functions Test Review Day 1
- LESSON 23: Functions Test Review Day 2
- LESSON 24: Functions Test